A T-MATRIX PERTURBATION FORMALISM FOR SCATTERING FROM A ROUGH FLUID-ELASTIC INTERFACE

Abstract

A perturbative representation of the null field T-matrix for scattering a pressure wave from a fluid elastic interface with surface roughness is developed. It is shown that thenth order T-matrix may be calculated recursively and expressed in terms of the elements of a zeroth order T-matrix. Further, it is shown that the expression for thenth order T-matrix is general in form and may be specialized to scattering from rigid and soft rough surfaces and from the rough surface of a fluid sediment. The T-matrix for thenth order spectral amplitude of the scattered pressure field in the fluid is calculated and its diagrammatic representation is constructed. For sinusoidal surface roughness, the perturbative representation of the T-matrix is used to calculate the spectral amplitudes of the Floquet modes of the pressure field scattered in the fluid. The results are compared with those obtained from a non-perturbative representation of the T-matrix and the accuracy and region of applicability of the formalism is determined. Then the relative scattering amplitudes of some of the individual scattering processes that occur in the diagrammatic representation of the T-matrix are calculated through second order. It is shown that diagrams that correspond to scalar processes in which surface pressure fields are excited and propagated tend to dominate diagrams that correspond to vector and tensor processes in which surface displacement fields are excited and propagated. A “scalar” approximation to the perturbation series is defined in which only scalar diagrams in the perturbation series are maintained. Numerical results for the perturbation series in the scalar approximation to fourth order are compared with exact results and it is shown that the scalar approximation provides reasonably accurate results for some applications.